I'll relate briefly my experience this year.
In December I moved to within 3-4 miles of work. Having been wanting to do a more Mustachian commute but never mustering up the 30mi ride I would have had before moving, I made a decision that from January 1st I would ride my bike to work every day.
January:
Week 1: I started biking to work, 3.5mi through residential neighborhoods and a small hill. Total elevation gain is around 100 ft for the entire ride. I noticed that when I got to work, I was tired, exhausted, I had what I called "zombie leg syndrome", which essentially means I walked like a zombie because my legs were so tired. To make matters worse I work on the 2nd floor and had also committed to never using the elevator.
Week 2: I do have a speedometer on my bike, so on the hill I would notice where my speed dropped. I started setting goals and trying to beat that spot. Monday went very well, but by Wednesday I was tired and stayed tired through Friday. Weekends were a blessing that I could just stay home and not ride.
Week 3: Monday is great again, legs are still suffering "zombie leg syndrome", but I feel a bit better. I am able to make it up further on the hill than I could last week before dropping below 10mph.
Week 4: Just keep at it, 3.5mi each way. Still have "zombie leg syndrome" when I get to work, but it's less than before.
February:
Week 1: Thursday was an awesome ride to work, blue skies above me, a bit chilly outside. Blizzard. Well, a Pacific Northwest Blizzard, which may just be a couple inches of snow, but half the office went home early, and by 4pm I've had multiple offers to take me home. I politely decline and spend my time googling how to ride in snow. I make it home safely, it was exhilirating. The next day I shamed myself and drove to work with the excuse that my wife wanted to go to Costco, so I drove her there first.
Week 2: Even with snow still on the ground it was easy enough to navigate and ride to work. Feeling better, speed hasn't improved much due to snow, but that is gone by Wednesday. I decided to stop timing myself on riding.
Week 3: Legs are a little tired getting to work, but I'm not quite as exhausted as before
Week 4: Monday is still my fastest day, but I begin to notice that it's not as hard as before. I think I was pushing too hard when timing myself and trying to race against myself every single day.
March:
Weather has gotten slightly better, not as cold. Riding more and decide I hate that small hill and am riding the car route home instead.
Ran a 5k.
April:
Going well, getting to work feels normal, no sign of exhaustion. Takes about 15 minutes.
June:
Ran another 5k, still no exhaustion from riding to work. Also biking to the grocery store, and the home improvement store.
Let's fast forward to September:
I found a cycling group. That hill I complained about before, I rode up it on the way to the meetup, did 17mph the whole way. Now I wonder why I thought it so hard. I generally hit 15-16mph average commuting 3.1mi (the car route is 0.4mi shorter), sometimes cruising down straight stretches at 22mph, maxing around 26mph on the one slight downhill section.
I started with a 17mi ride with the group, completely exhausted afterwards, the next day riding to work was slow. Went back the next week, did another 19mi route. For September I averaged around 80mi a week. I also got a friend started on cycling.
October:
Started going on as many rides as I could, eventually working up to doing 56mi in one day this month. Averaged 120mi/week.
I started at 220lbs, and am now 196lbs, at 5'10". Diet will get you further on weight loss, but I feel more fit now than ever before. My resting pulse has dropped, my blood pressure is almost back down to normal.